mpn/generic/toom3_sqr.c

/* mpn_toom3_sqr -- Square {ap,an}.

   Contributed to the GNU project by Torbjorn Granlund.
   Additional improvements by Marco Bodrato.

   THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE.  IT IS ONLY
   SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
   GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.

Copyright 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.

This file is part of the GNU MP Library.

The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The GNU MP Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */


#include "gmp.h"
#include "gmp-impl.h"

/* Evaluate in: -1, 0, +1, +2, +inf

  <-s--><--n--><--n-->
   ____ ______ ______
  |_a2_|___a1_|___a0_|

  v0  =  a0         ^2 #   A(0)^2
  v1  = (a0+ a1+ a2)^2 #   A(1)^2    ah  <= 2
  vm1 = (a0- a1+ a2)^2 #  A(-1)^2   |ah| <= 1
  v2  = (a0+2a1+4a2)^2 #   A(2)^2    ah  <= 6
  vinf=          a2 ^2 # A(inf)^2
*/

#if TUNE_PROGRAM_BUILD
#define MAYBE_sqr_basecase 1
#define MAYBE_sqr_toom3   1
#else
#define MAYBE_sqr_basecase						\
  (SQR_TOOM3_THRESHOLD < 3 * SQR_TOOM2_THRESHOLD)
#define MAYBE_sqr_toom3							\
  (SQR_TOOM4_THRESHOLD >= 3 * SQR_TOOM3_THRESHOLD)
#endif

#define TOOM3_SQR_REC(p, a, n, ws)					\
  do {									\
    if (MAYBE_sqr_basecase						\
	&& BELOW_THRESHOLD (n, SQR_TOOM2_THRESHOLD))			\
      mpn_sqr_basecase (p, a, n);					\
    else if (! MAYBE_sqr_toom3						\
	     || BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD))		\
      mpn_toom2_sqr (p, a, n, ws);					\
    else								\
      mpn_toom3_sqr (p, a, n, ws);					\
  } while (0)

void
mpn_toom3_sqr (mp_ptr pp,
	       mp_srcptr ap, mp_size_t an,
	       mp_ptr scratch)
{
  mp_size_t n, s;
  mp_limb_t cy, vinf0;
  mp_ptr gp;
  mp_ptr as1, asm1, as2;

#define a0  ap
#define a1  (ap + n)
#define a2  (ap + 2*n)

  n = (an + 2) / (size_t) 3;

  s = an - 2 * n;

  ASSERT (0 < s && s <= n);

  as1 = scratch + 4 * n + 4;
  asm1 = scratch + 2 * n + 2;
  as2 = pp + n + 1;

  gp = scratch;

  /* Compute as1 and asm1.  */
  cy = mpn_add (gp, a0, n, a2, s);
#if HAVE_NATIVE_mpn_add_n_sub_n
  if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
    {
      cy = mpn_add_n_sub_n (as1, asm1, a1, gp, n);
      as1[n] = cy >> 1;
      asm1[n] = 0;
    }
  else
    {
      mp_limb_t cy2;
      cy2 = mpn_add_n_sub_n (as1, asm1, gp, a1, n);
      as1[n] = cy + (cy2 >> 1);
      asm1[n] = cy - (cy2 & 1);
    }
#else
  as1[n] = cy + mpn_add_n (as1, gp, a1, n);
  if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
    {
      mpn_sub_n (asm1, a1, gp, n);
      asm1[n] = 0;
    }
  else
    {
      cy -= mpn_sub_n (asm1, gp, a1, n);
      asm1[n] = cy;
    }
#endif

  /* Compute as2.  */
#if HAVE_NATIVE_mpn_rsblsh1_n
  cy = mpn_add_n (as2, a2, as1, s);
  if (s != n)
    cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
  cy += as1[n];
  cy = 2 * cy + mpn_rsblsh1_n (as2, a0, as2, n);
#else
#if HAVE_NATIVE_mpn_addlsh1_n
  cy  = mpn_addlsh1_n (as2, a1, a2, s);
  if (s != n)
    cy = mpn_add_1 (as2 + s, a1 + s, n - s, cy);
  cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n);
#else
  cy = mpn_add_n (as2, a2, as1, s);
  if (s != n)
    cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
  cy += as1[n];
  cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
  cy -= mpn_sub_n (as2, as2, a0, n);
#endif
#endif
  as2[n] = cy;

  ASSERT (as1[n] <= 2);
  ASSERT (asm1[n] <= 1);

#define v0    pp				/* 2n */
#define v1    (pp + 2 * n)			/* 2n+1 */
#define vinf  (pp + 4 * n)			/* s+s */
#define vm1   scratch				/* 2n+1 */
#define v2    (scratch + 2 * n + 1)		/* 2n+2 */
#define scratch_out  (scratch + 5 * n + 5)

  /* vm1, 2n+1 limbs */
#ifdef SMALLER_RECURSION
  TOOM3_SQR_REC (vm1, asm1, n, scratch_out);
  cy = 0;
  if (asm1[n] != 0)
    cy = asm1[n] + mpn_add_n (vm1 + n, vm1 + n, asm1, n);
  if (asm1[n] != 0)
    cy += mpn_add_n (vm1 + n, vm1 + n, asm1, n);
  vm1[2 * n] = cy;
#else
  TOOM3_SQR_REC (vm1, asm1, n + 1, scratch_out);
#endif

  TOOM3_SQR_REC (v2, as2, n + 1, scratch_out);	/* v2, 2n+1 limbs */

  TOOM3_SQR_REC (vinf, a2, s, scratch_out);	/* vinf, s+s limbs */

  vinf0 = vinf[0];				/* v1 overlaps with this */

#ifdef SMALLER_RECURSION
  /* v1, 2n+1 limbs */
  TOOM3_SQR_REC (v1, as1, n, scratch_out);
  if (as1[n] == 1)
    {
      cy = as1[n] + mpn_add_n (v1 + n, v1 + n, as1, n);
    }
  else if (as1[n] != 0)
    {
#if HAVE_NATIVE_mpn_addlsh1_n
      cy = 2 * as1[n] + mpn_addlsh1_n (v1 + n, v1 + n, as1, n);
#else
      cy = 2 * as1[n] + mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2));
#endif
    }
  else
    cy = 0;
  if (as1[n] == 1)
    {
      cy += mpn_add_n (v1 + n, v1 + n, as1, n);
    }
  else if (as1[n] != 0)
    {
#if HAVE_NATIVE_mpn_addlsh1_n
      cy += mpn_addlsh1_n (v1 + n, v1 + n, as1, n);
#else
      cy += mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2));
#endif
    }
  v1[2 * n] = cy;
#else
  cy = vinf[1];
  TOOM3_SQR_REC (v1, as1, n + 1, scratch_out);
  vinf[1] = cy;
#endif

  TOOM3_SQR_REC (v0, ap, n, scratch_out);	/* v0, 2n limbs */

  mpn_toom_interpolate_5pts (pp, v2, vm1, n, s + s, 0, vinf0);
}